Question

What is the biggest area of a quadrilateral you can fit in a circle that has a

Answer 1

Answer: 200 square units

Step-by-step explanation:

Given

Circumference of the circle is $20\pi$

Suppose r is the radius of the circle

The biggest area of a quadrilateral that can fit in a circle is of square.

Deduce the radius of the circle

$2\pi r=20\pi\\r=10\ \text{units}$

Suppose the side of the square is a

from the figure, we can write

$\Rightarrow a^2+a^2=(2r)^2\\\Rightarrow 2a^2=4r^2\\\Rightarrow a=\sqrt{2}r\\\Rightarrow a=10\sqrt{2}\ \text{units}$

Area of the quadrilateral is

$\Rightarrow A=(10\sqrt{2})^2\\\Rightarrow A=100\times 2\\\Rightarrow A=200\ \text{square units}$